Trade Statistics: Which deviation to use?

bdixon619 · Aug 15, 2003

Quote from BKuerbs:

..
So Mr. Zones swings an average $300 trade. His variance is equal to $36. ...

It is an example, I know: But an average of $300 and a variance of $36?

Even if you had written "a standard deviation of $36" I would suggest another name for that trader......

Have a nice day

Bernd Kuerbs

Hi Bernd,

What would that be?

Bruce

BKuerbs · Aug 15, 2003

@bdixon619

Guess yourself...

I assume we are talking of more than hundred real trades and not backtested stuff: $300 average and a standard dev of $36 then essentailly means no losing trades, (nearly)always winning, (nearly) always gaining $300.

The coefficient of variation would be 12%, some hundred percent are common in the markets.

regards

Bernd Kuerbs

bdixon619 · Aug 15, 2003

Quote from BKuerbs:

@bdixon619

Guess yourself...

I assume we are talking of more than hundred real trades and not backtested stuff: $300 average and a standard dev of $36 then essentailly means no losing trades, (nearly)always winning, (nearly) always gaining $300.

The coefficient of variation would be 12%, some hundred percent are common in the markets.

regards

Bernd Kuerbs

I was really looking for your suggestion...I like Swing's name. As to my hypothetical report of his performance, maybe Mr. Efficiency would suit him...I'm only guessing because you asked though.

Using ES as a vehicle and playing for 1 pt. is might be possible with multiple contracts and tight stops. But i was just grabbing at numbers to illustrate the use of Chebyshev's inequality, not make a statement about what Swing might actually be capable of doing.

Bruce

agrau · Aug 15, 2003

Copied from Numerical Recipes in C, which is probably not the ultimate authority in statistics, but maybe interesting nevertheless:

As the mean depends on the first moment of variance and standard deviation depend on the second moment. It is not uncommon, in real life, to be dealing with a distribution whose second moment does not exist (i.e., is infinite). In this case, the variance or standard deviation is useless as a measure of the dataâs width around its central value: The values obtained from equations (14.1.2 - Variance) or (14.1.3- Standard Deviation) will not converge with increased numbers of points, nor show any consistency from data set to data set drawn from the same distribution. This can occur even when the width of the peak looks, by eye, perfectly finite. A more robust estimator of thewidth is the average deviation or mean absolute deviation, defined by [ ... formula didn't copy, sorry].

One often substitutes the sample median xmed for x in equation (14.1.4 - Average Deviation). For any fixed sample, the median in fact minimizes the mean absolute deviation.

Statisticians have historically sniffed at the use of (14.1.4 - Average Deviation) instead of (14.1.2 - Standard Deviation), since the absolute value brackets in (14.1.4) are ânonanalyticâ and make theorem-proving difficult. In recent years, however, the fashion has changed, and the subject of robust estimation (meaning estimation for broad distributions with significant numbers of âoutlierâ points) has become a popular and important one. Higher moments, or statistics involving higher powers of the input data, are almost always less robust than lower moments or statistics that involve only linear sums or (the lowest moment of all) counting.

It was these line that made me think, if it would be always the best to use STDEV, but it seems everybody uses it. Why is this so? Some synapses got connected today reminding me of the years, when just everybody "knew", that spinachi contained lots and lots of iron. Are we copying here again, non-reflecting if STDEV is the best choice?

To me, it seems there are different deviations, each having their specific properties and pros/cons. If I am right with this assumption, would it be far-fetched to try to take the most useful use of these properties, i.e. depending on what one is looking at, taking one or the other.

Andreas

Mr Subliminal · Aug 15, 2003

As the mean depends on the first moment of variance and standard deviation depend on the second moment.

You may have been right about your source - the mean depending on the first moment of variance?! Hardly. This doesn't, however, diminish the explanation of average deviation which follows. Thanks for that.

Quote from agrau
To me, it seems there are different deviations, each having their specific properties and pros/cons. If I am right with this assumption, would it be far-fetched to try to take the most useful use of these properties, i.e. depending on what one is looking at, taking one or the other.

How large is the difference between the different deviations? For trading systems in general, and risk of ruin and position sizing calculations in particular, I would strongly advise erring on the side of safety. You have the perfect opportunity

agrau · Aug 16, 2003

Quote from Mr Subliminal:
How large is the difference between the different deviations? For trading systems in general, and risk of ruin and position sizing calculations in particular, I would strongly advise erring on the side of safety. You have the perfect opportunity
[/B]

Completely agree with wanting to err on the safe side.

For the sake of discussion, let's say there is a trend-following system with good stop-losses. Thus having many small losses and a some large wins. When looking at risk, my interest lays on the left side of the distribution - how bad can it go. Sure, one can pick the Stdev and by this is on the safe side. But knowing the variance around the observed "normal", i.e. removing positive outliers, would be more descriptive. Anybode is free to adjust this deviation by some number to inflate the theoretical risk for money management purposes.

My thinking follows one chapter in Taleb's book, where he says that the mean is not the rule. Having an asymetric distribution, the mean is not the average, and he brings skewness into the game.

Would be interesting to hear about money management schemes that take the skew into account. Anybody?

Best, Andreas

agrau · Aug 16, 2003

Another earlier discussion on this:

http://www.elitetrader.com/vb/showthread.php?s=&threadid=11149

harrytrader · Aug 16, 2003

I used Tchebycheff for his name as for myself. As for the formula I use it everyday as illustrated in an old post:

http://www.elitetrader.com/vb/showthread.php?s=&postid=261059&highlight=Tcheby*#post261059

Quote from bdixon619:

Bruce, I think the distribution of the different versions of his name warrants a formula of its own. I found 9!!

"Chebyshev or Tchebycheff
Pafnuty Lvovich Chebyshev was a notable Russian mathematician, who was born on 16 May 1821 and died on 8 December 1894. He wrote on number theory, analysis, probability, mechanics and maps.

Bruce